Structures on self-adjoint vertex conditions of local Sturm-Liouville operators on graphs (Q283603)

This work deals with the vertex conditions of local Sturm-Liouville operators on metric graphs. The authors give a new description of vertex conditions defining the self-adjoint Sturm-Liouville operators and clarify the natural geometric structure on the space of complex vertex conditions. Moreover, based on this description, they provide self-adjointness results for local Sturm-Liouville operators on finite graphs and the Povzner-Wienholtz-type self-adjointness results for local Sturm-Liouville operators on infinite graphs. The results obtained in this paper are interesting and new.